Advances in human brain neuroimaging for high-temporal and high-spatial resolution will depend on localization of Electroencephalography (EEG) signals to their cortex sources. The source localization inverse problem is inherently ill-posed and depends critically on the modeling of human head electromagnetics. We present a systematic methodology to analyze the main factors and parameters that affect the EEG source-mapping accuracy. These factors are not independent and their effect must be evaluated in a unified way. To do so requires significant computational capabilities to explore the problem landscape, quantify uncertainty effects, and evaluate alternative algorithms. Bringing high-performance computing (HPC) to this domain is necessary to open new avenues for neuroinformatics research. The head electromagnetics forward problem is the heart of the source localization inverse. We present two parallel algorithms to address tissue inhomogeneity and impedance anisotropy. Highly-accurate head modeling environments will enable new research and clinical neuroimaging applications. Cortex-localized dEEG analysis is the next-step in neuroimaging domains such as early childhood reading, understanding of resting state brain networks, and models of full brain function. Therapeutic treatments based on neurostimulation will also depend significantly on HPC integration.